Some remarks on the Banach space valued Hilbert transform
type: Item
instance of: scholarly article
title: Some remarks on the Banach space valued Hilbert transform
zbMATH Open document ID: 0776.47013
DOI: 10.1016/0019-3577(91)90030-B
author: B. de Pagter
author: Philippe Clément
published in: Indagationes Mathematicae. New Series
publication date: 1992-09-27T00:00:00Z
review text: The authors give an elementary proof of the boundedness of the Banach space valued Hilbert transform for the spaces \(L_ p(\Omega,L_ q(\Sigma))\), where \(1<p,q<\infty\) and \(\Omega\), \(\Sigma\) are \(\sigma\)- finite measure spaces. The main step is an extension to the vector-valued case of a proof, due to Bochner, of the continuity of the Riesz projection in \(L_ p(0,1)\).
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 42B20
zbMATH DE Number: 60867
zbMATH Keywords: boundedness of the Banach space valued Hilbert transform
zbMATH Keywords: continuity of the Riesz projection
reviewed by: M. González
MaRDI profile type: Publication
cites work: CONVOLUTION OPERATORS ON BANACH SPACE VALUED FUNCTIONS
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full work available at URL: 0019-3577(91)90030-b
OpenAlex ID: W2088375748
description: scientific article; zbMATH DE number 60867